Prayer

A Jew must pray, three times daily. We also find, that the Halacha relates to non-Jews as well.

The Talmud (Sanhedrin 56a) teaches us, that the sons of Noah were commanded seven precepts, known as the Noachide Laws (sheva mitzvot Bnei Noach).
The source for these seven laws, is a pasuk (verse) in Bereishit (2:16).

Who has to observe these seven laws? All the people in the world, since they are the descendants of Noah

Over the course of time, the Noachide Laws were forgotten by the nations of the world, and they began to worship differently.
______
Rav Moshe Feinstein, zt"l, dealt with this question, in his Igrot Moshe (Orach Chayyim, chelek 2, siman 24).

He cites a pasuk from Isaiah (56:7), ('Ki [B]eiti beit tefillah yikarei lechol ha'amim), for My house (i.e., the Beit Hamikdash) shall be called, a house of prayer, for all peoples.'

Rashi ad loc. Remarks, that this means, that the Temple will serve as a house of prayer, not only for Jews.

Bnei Noach, can earn a merit, when they pray to G-d.

In such a case, it is incumbent upon him to pray, since the fundamental principle of the Noachide Laws, is belief in G-d; and by praying for a specific need, the Ben Noach manifests his trust in G-d, as the source and provider of his needs.

Were he not to pray in such a situation, it would show, that he does not believe in G-d.

The Noachide Laws are predicated on the belief, that G-d commanded them, to folow these Laws.
_________
A novel approach to this question was taken by the Lubavitcher Rebbe, Rav Menachem Mendel Schneerson,
in a talk delivered during a Farbrengen on Simchat Torah 5746 (1985)

[see also Sichot in English, vol. 21, pp. 290-300, and vol. 8, pp. 198-202].
_________
He advocated a neutral 'moment of silence,' not a prayer, which would not violate the principle of separation of religion and state; and at the same time, would not expose Jewish children in public schools to a text, that might be questionable.
It would, however, require parents to explain to their children, the objective of this 'moment of silence.'

He stressed, it would have to take place at the start of the school day, when the children are not yet distracted by other matters.

There are many parents, Jews and gentiles alike, who want their children to grow up to be responsible human beings, and that a 'moment of silence' is the 'last hope' to achieve this.